🍕 Mixed Numbers
Cambridge Lower Secondary · Grade 7 · Fractions & Decimals
Mixed ↔ Improper
2 3⁄4 = 11/4
(2 × 4 + 3) over 4
Adding Mixed Numbers
1 1⁄3 + 2 1⁄2 = 3 5⁄6
Find common denominator, add parts
Multiply & Divide
1 1⁄2 × 2 2⁄3 = 4
Convert to improper first!
See what 2 ¾ pizzas looks like! 🍕
Two whole pies + ¾ of a pie = 2 ¾
What you'll learn:
- Converting mixed numbers ↔ improper fractions
- Adding mixed numbers (same and different denominators)
- Subtracting with borrowing/regrouping
- Multiplying mixed numbers (convert first!)
- Dividing mixed numbers (KCF method)
- Ordering mixed numbers on a number line
- Problem solving in real contexts
📖 Learn: Mixed Numbers
Part 1: What is a Mixed Number?
A mixed number has a whole part and a fraction part: e.g. 2 ¾ = 2 wholes and ¾ of another whole.
An improper fraction has a numerator bigger than (or equal to) the denominator: e.g. 11/4.
Mixed → Improper: multiply whole by denominator, add numerator, keep denominator.
2 ¾ → (2 × 4 + 3) / 4 = 11/4
Improper → Mixed: divide numerator by denominator. Quotient = whole, remainder = new numerator.
11 ÷ 4 = 2 remainder 3 → 2 ¾
🍕 Pizza model: 11/4 means 11 slices with 4 per pizza. 11 ÷ 4 = 2 full pizzas + 3 slices left = 2 ¾
Part 2: Adding Mixed Numbers
Same denominator: Add whole parts, add fraction parts, simplify if needed.
1 ²⁄₅ + 2 ¹⁄₅ = (1+2) + (2+1)/5 = 3 ³⁄₅
2 ³⁄₅ + 1 ⁴⁄₅ = 3 ⁷⁄₅ → ⁷⁄₅ = 1 ²⁄₅ → answer: 4 ²⁄₅ (regroup when fraction ≥ 1)
Different denominators: Find LCM, convert fraction parts, then add.
1 ¹⁄₃ + 2 ¹⁄₂ → LCM(3,2) = 6 → 1 ²⁄₆ + 2 ³⁄₆ = 3 ⁵⁄₆
💡 You can also convert both to improper fractions, add, then convert back — same answer!
Part 3: Subtracting Mixed Numbers (with Borrowing)
No borrowing needed: Subtract fraction parts (same denominator), subtract whole parts.
3 ⁴⁄₅ − 1 ²⁄₅ = 2 ²⁄₅
Borrowing (regrouping): When the fraction to subtract is bigger than what you have, borrow 1 whole from the whole number.
4 ¹⁄₃ − 1 ²⁄₃
¹⁄₃ < ²⁄₃, so borrow: 4 ¹⁄₃ = 3 ⁴⁄₃ (borrow 1 whole = ³⁄₃, add to ¹⁄₃)
3 ⁴⁄₃ − 1 ²⁄₃ = 2 ²⁄₃
🍕 Imagine: you need 2 slices but only have 1. Break open a whole pizza into 3 slices — now you have 4 slices!
Part 4: Multiplying Mixed Numbers
Always convert to improper fractions first, then multiply top × top, bottom × bottom, simplify.
1 ½ × 2 ²⁄₃ → ³⁄₂ × ⁸⁄₃ = 24/6 = 4
2 ¼ × 1 ¹⁄₃ → ⁹⁄₄ × ⁴⁄₃ = 36/12 = 3 → 3
💡 Cross-cancel before multiplying to keep numbers small: ⁹⁄₄ × ⁴⁄₃ → the 4s cancel → ³⁄₁ × ¹⁄₁ = 3
Part 5: Dividing Mixed Numbers (KCF)
Keep · Change · Flip: Convert to improper, Keep the first, Change ÷ to ×, Flip the second.
2 ½ ÷ 1 ¼ → ⁵⁄₂ ÷ ⁵⁄₄ → ⁵⁄₂ × ⁴⁄₅ = 20/10 = 2
3 ¹⁄₃ ÷ 2 → ¹⁰⁄₃ ÷ ²⁄₁ → ¹⁰⁄₃ × ¹⁄₂ = 10/6 = 5/3 = 1 ²⁄₃
🔑 K·C·F: Keep the first fraction, Change ÷ to ×, Flip (reciprocal) the second fraction.
💡 Worked Examples
Example 1: Converting Mixed ↔ Improper
(a) Convert 3 ²⁄₅ to an improper fraction.
Step 1: Multiply whole × denominator: 3 × 5 = 15
Step 2: Add numerator: 15 + 2 = 17
Step 3: Keep denominator: 17/5
(b) Convert 19/6 to a mixed number.
Step 1: 19 ÷ 6 = 3 remainder 1
Step 2: Whole = 3, remainder 1 over denominator 6
Answer: 3 ¹⁄₆
✅ Check: 3 × 6 + 1 = 19 ✔
Example 2: Adding Mixed Numbers (Different Denominators)
Calculate 2 ¹⁄₄ + 1 ²⁄₃
Step 1: LCM(4, 3) = 12
Step 2: Convert: ¹⁄₄ = ³⁄₁₂ ²⁄₃ = ⁸⁄₁₂
Step 3: Add: 2 ³⁄₁₂ + 1 ⁸⁄₁₂ = 3 ¹¹⁄₁₂
Answer: 3 ¹¹⁄₁₂
💡 ¹¹⁄₁₂ < 1, so no regrouping needed here.
Example 3: Subtracting with Borrowing
Calculate 5 ¹⁄₄ − 2 ¾
Step 1: Same denominator (4). Is ¼ < ¾? Yes — must borrow!
Step 2: Borrow 1 whole from 5: 5 ¼ → 4 ⁵⁄₄ (add ⁴⁄₄ to ¼)
Step 3: 4 ⁵⁄₄ − 2 ¾ = (4−2) + (5−3)/4 = 2 ²⁄₄ = 2 ½
Answer: 2 ½
🍕 Breaking a whole pizza into 4 slices gives us enough slices to subtract!
Example 4: Multiplying & Dividing Mixed Numbers
(a) Calculate 1 ¾ × 2 ²⁄₅
Step 1: Convert: 1 ¾ = ⁷⁄₄ 2 ²⁄₅ = ¹²⁄₅
Step 2: Multiply: ⁷⁄₄ × ¹²⁄₅ = 84/20 = 21/5
Step 3: 21 ÷ 5 = 4 r 1 → 4 ¹⁄₅
(b) Calculate 3 ½ ÷ 1 ¼
Step 1: Convert: 3 ½ = ⁷⁄₂ 1 ¼ = ⁵⁄₄
Step 2: KCF: ⁷⁄₂ × ⁴⁄₅ = 28/10 = 14/5
Step 3: 14 ÷ 5 = 2 r 4 → 2 ⁴⁄₅
🔑 Always K·C·F for division. Never try to divide fractions directly.
🍕 Pizza Visualizer & Conversion Game
Pizza Model — see mixed number operations animated!
🎮 Conversion Catcher — click the correct mixed number before the card falls!
Score: 0
Lives: ❤️❤️❤️
Level: 1
📏 Number Line Placer — drag cards to their correct positions!
Click a card from the pool, then click the target slot on the number line.
✏️ Exercise 1: Converting Mixed ↔ Improper
Type your answer as an improper fraction (e.g. 11/4) or mixed number (e.g. 2 3/4).
✏️ Exercise 2: Adding Mixed Numbers
Give your answer as a mixed number or improper fraction in lowest terms.
✏️ Exercise 3: Subtracting Mixed Numbers (with Borrowing)
Watch borrowing happen step-by-step!
Example: 4 ¹⁄₃ − 1 ²⁄₃
Step 1: Compare fractions: ¹⁄₃ < ²⁄₃ — we must borrow!
Step 2: Borrow 1 whole from the 4:
4 ¹⁄₃ becomes 3 ⁴⁄₃ (3 wholes + ³⁄₃ + ¹⁄₃ = 3 + ⁴⁄₃)
Step 3: Subtract: 3 ⁴⁄₃ − 1 ²⁄₃ =
2 ²⁄₃
Now practise — give your answer as a mixed number or fraction.
✏️ Exercise 4: Multiplying & Dividing Mixed Numbers
Convert to improper first! Give your answer as a mixed number or improper fraction.
📏 Exercise 5: Ordering & Word Problems
Part A — Order from smallest to largest
Click cards from the pool to place them in order. Click a placed card to remove it.
Part B — Word Problems